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@CodyGray I have probably 80+ vintage computers. Last time I counted was 2-3 years ago and it was 56 IIRC then. I'm working on building an inventory system because I lost count! Anyway, I mostly get them off eBay. A few have been given to me and I've bought a few from Craigslist. But a vast majority of them have been eBay finds.
– cbmeeksJul 28 '17 at 18:30

Sounds like a short - have you tried disconnecting the board and measuring the PSU by itself? Don't let it run like this for more than a minute, it probably doesn't like zero load.
– Zac67Jul 28 '17 at 18:31

@Zac67 yes, I've tested just the PSU with nothing on it at all and I still hear the clicking.
– cbmeeksJul 28 '17 at 18:35

Could still be caps - the ticking might hint to a switching PSU that does not properly start oscillating
– tofroJul 28 '17 at 20:44

2 Answers
2

The ticking indicates restarting of the power supply by the controller, probably
due to a short. The short would have to be on the OUTPUT (low voltage) side
(shorted AC-side devices would have taken the fuse out).

Power supplies of that era didn't suffer burst capacitors as often as the post-2000 years. The most likely cause of overcurrent is a shorted fast-recovery diode in a DC output circuit.

Look at CR51 ("C82M") and CR52 ("B82M"), one of those is probably shorted (either side pin to
the center should read as a diode, center=cathode).

A suitable replacement (has to be fully insulated "fullpak") without the Japanese part number (because TDK made these supplies) might be MBRF2045CTG, from ON Semiconductor.
The same power supply was in LC, LCII, Performa 4nn, Quadra 605... but there
were earlier versions as well, so my part numbers might not be the same as yours.

I have a LC with no bad caps in the power supply but a lot of cracked soldering pins, especially around components which generate a lot of heat. This can result in a multitude of erratic behavior. I recommend to re-solder the whole board. Take care of component pins which have a thick oxide coating because of prolonged exposure to heat in a cracked solder spot. If re-soldering this particular component doesn't look as expected, take out the part and scratch the pin blank. Apply solder and put it in again.